Euclid's Construction of a Regular Dodecahedron (XIII.17)
Let and be the centers of the two adjacent cube faces and with common side , and let , , , and be the midpoints of , , , and .[more]
, , and are points that satisfy the golden section conditions , , and .
and are perpendicular to , is perpendicular to , and .
is one face of a regular dodecahedron.
The other faces are constructed in the same way.[less]
For more information, see http://aleph0.clarku.edu/~djoyce/java/elements/bookXIII/propXIII17.html.